Physics Letters B 662 (2008) 185–189

www.elsevier.com/locate/physletb

Probing a supersymmetric model for neutrino massesat ultrahigh energy neutrino telescopes

M. Hirsch a, D.P. Roy a,b,∗, J.W.F. Valle a

a AHEP Group, Instituto de Fisica Corpuscular (IFIC), CSIC-U. de Valencia, Edificio de Instituto de Paterna,Apartado de Correos 22085, E-46071 Valencia, Spain

b Homi Bhabha Centre for Science Education, Tata Institute of Fundamental Research, Mumbai 400088, India

Received 19 December 2007; received in revised form 26 February 2008; accepted 28 February 2008

Available online 7 March 2008

Editor: A. Ringwald

Abstract

A bilinear R-parity breaking SUSY model for neutrino mass and mixing predicts the lightest superparticle to decay mainly into a pair of tauleptons or b quarks along with a neutrino for relatively light SUSY spectra. This leads to a distinctive triple bang signature of SUSY events atultrahigh energy neutrino telescopes like IceCube or Antares. While the expected signal size is only marginal at IceCube, it will be promising fora future multi-km3 size neutrino telescope.© 2008 Elsevier B.V. All rights reserved.

There is a good deal of current interest in the R-parity break-ing SUSY models of neutrino mass and mixing, since they si-multaneously provide a solution to the hierarchy problem of thestandard model [1]. Besides they are amenable to direct exper-imental test in the foreseeable future unlike the canonical see-saw models. In particular the bilinear R-parity breaking SUSYmodel has relatively few RPB parameters, which can be fixed interms of the observed neutrino masses and mixing angles [2–6].Therefore it offers a predictive and well motivated extension ofthe minimal supersymmetric Standard Model (MSSM). It is de-scribed by the superpotential

(1)W = WMSSM + εiLiHu,

with three extra parameters describing the bilinear RPB cou-pling of the three generations of leptons to the u-type Higgssuperfield. In addition there are three new parameters to de-scribe the new soft supersymmetry breaking terms

(2)V = VMSSM + Biεi liHu.

* Corresponding author at: Homi Bhabha Centre for Science Education, TataInstitute of Fundamental Research, Mumbai 400088, India.

E-mail address: dproy1@gmail.com (D.P. Roy).

0370-2693/$ – see front matter © 2008 Elsevier B.V. All rights reserved.doi:10.1016/j.physletb.2008.02.065

All the six RPB parameters are determined within fairly tightlimits from the observed neutrino masses and mixing angles,so that one has effectively no free parameters other than thoseof the MSSM [5,6]. Moreover the small neutrino masses en-sure very small RPB parameters εi , so that all the predictionsof superparticle production and decay down to the LSP remainessentially the same as in the MSSM. But the LSP is predictedto decay with the decay range and branching ratios determinedin terms of the above mentioned RPB parameters. The detailsof these predictions may be found in Ref. [6]. We shall onlymention here the two main features of LSP decay, which shallbe used in our analysis. Firstly the main decay channels of theLSP (χ ) are (A) χ → τ+τ−ν and (B) χ → bbν, with branchingratios of about 0.3 and 0.6 respectively over the relatively lightSUSY mass range of our interest. Secondly its decay range,r0 = cτ , is about 1 mm for mχ

∼= 100 GeV and goes down in-versely as its mass thereafter.

The first feature implies a strong degradation of the canoni-cal missing-pT signature of the R-parity conserving MSSM atthe LHC. Nonetheless one can get viable leptonic signatures forsuperparticle production at LHC from their cascade decay viawino into a bino LSP in the mSUGRA model, where one has a2 : 1 hierarchy between the wino and bino masses [7]. On theother hand in a more general MSSM the two masses can be of

186 M. Hirsch et al. / Physics Letters B 662 (2008) 185–189

roughly similar size, in which case it will be hard to get a viablesignature at the LHC.

We investigate here the signature of such a bilinear RPBSUSY model at an ultrahigh energy neutrino telescope like Ice-Cube [8] or a water Cerenkov telescope of similar size in theMediterranean [9]. To be definitive we shall consider three setsof MSSM spectra:

(I) mχ∼= 100 GeV, m

W∼= m

Z∼= m

l∼= 120 GeV, mq

∼=150 GeV,

(II) mχ∼= 120 GeV, m

W∼= m

Z∼= m

l∼= 140 GeV, mq

∼=200 GeV,

(III) mχ∼= 120 GeV, m

W∼= m

Z∼= m

l∼= 250 GeV, mq

∼=300 GeV.

Admittedly the sets I and II represent relatively light spar-ticle masses, chosen to give favourable signal cross-sections.However, for the same reason they represent the most favoura-ble superparticle spectra from naturalness consideration. More-over, these two cases will be hard to probe at LHC in the RPBSUSY model because of the degradation of the missing-pT aswell as the pT of the leptons coming from the cascade decay.For the same reason the Tevatron limit on squark masses donot apply to them, while they satisfy all the LEP limits [10].Thus they represent a very important region of the MSSM pa-rameter space, to be probed at the UHE neutrino telescopes. Onthe other hand the set III represents relatively high wino, zinoand slepton masses, like the typical mSUGRA spectrum for theelectroweak sector. Thanks to the 2 : 1 mass hierarchy betweenthe wino and the bino (LSP), this case can be probed at LHCvia the leptonic signature [7].

The SUSY signals of our interest come from the CC and NCprocesses

(3)νqW→ lq, l → lχ,

(4)νqZ→ νq, ν → νχ,

followed by the decay of χ into channels A or B above. Thecross-sections can be easily obtained from the correspondingones derived in [11,12] for electro-production. As in Ref. [11]we shall neglect mixings for chargino and neutralino states,which we expect to be good approximations as long as the hig-gsino states are reasonably heavy relative to the wino and zino.The different helicity contributions to the CC process (3) aregiven by

dσLL,RRCC

dt= πα2

Sin4 θW

m2W

s(t − m2W

)2;

(5)dσ

LR,RLCC

dt= πα2

Sin4 θW

(tu − m2lm2

q)

s2(t − m2W

)2.

The corresponding contributions to the NC process (4) are ob-tained by substituting the zino mass for the wino and multiply-ing by the coupling factor G

qL,R/Cos4 θW , where

Gq = (

0.5 − eq Sin2 θW

)2 and

L

(6)GqR = (

eq Sin2 θW

)2.

The resulting signal cross-sections are obtained by convolutingthese CC and NC cross-sections with the corresponding quarkdensities, i.e.

σCC =1∫

xmin

dx

tmin∫tmax

dt

(πα2

4 Sin4 θW

)[m2

W

s(t − m2W

)2

∑i

di(x)

(7)+ di (x) +(tu − m2

lm2

q)

s2(t − m2W

)2

∑i

ui(x) + ui (x)

],

σNC =1∫

xmin

dx

tmin∫tmax

dt

(πα2

2 Sin4 θW Cos4 θW

)

×[

m2Z

s(t − m2Z)2

∑i

(Gu

Lui(x) + GuRui(x)

+ GdLdi(x) + Gd

Rdi(x))

+(tu − m2

lm2

q)

s2(t − m2Z)2

∑i

(Gu

Lui(x) + GuRui(x)

(8)+ GdLdi(x) + Gd

Rdi(x))]

where i is the generation index and

tmin,max = −(s − m2

l− m2

q ∓√(

s − m2l− m2

q

)2 − 4m2lm2

q

)/2;(9)xmin = (m

l+ mq)2/2Eνm.

Due to the large squark and slepton masses the minimum x forthe SUSY processes is at least four orders of magnitude largerthan that for the SM CC processes like

(10)ντ qW→ τq ′,

and the strong rise of the sea quark densities at low x impliesthat the cross-sections for the SUSY processes (3), (4) are sup-pressed by at least two orders of magnitude relative to this SMCC cross-section.

We have computed the SUSY signal cross-section from theCC and NC processes (3), (4) using the CTEQ4L quark densi-ties, setting the scale Q2 = s. We have also checked that thereis very little change in the result for alternative choices of scaleor quark densities.

Fig. 1 shows the SUSY signal cross-sections for the MSSMspectra of sets I, II and III over the UHE neutrino energy rangeEν = 10–1000 PeV. Our cross-section for the set III matcheswith the corresponding cross-section computed recently [13],in the context of a different extension of the MSSM. For com-parison we also show the leading order SM CC cross-sectionusing the simple parametrisation of [14], i.e.

(11)σ SMCC = 5.53 pb(Eν/GeV)0.363.

The NLO correction along with uncertainty of quark densitiescan change this cross-section by about 30% [15]. The SM CC

M. Hirsch et al. / Physics Letters B 662 (2008) 185–189 187

Fig. 1. Signal cross-sections for SUSY spectra I (solid), II (dashed) andIII (dot-dashed) shown against the neutrino energy along with the SM CCcross-section (top line).

Fig. 2. The Lorentz boosted range of the LSP (dotted) shown along with thoseof the more (solid) and less (dot-dashed) energetic decay taus. The lines fromtop to bottom represent the SUSY spectra I, II and III, respectively.

cross-section is indeed seen to be larger than the SUSY cross-sections of sets I–III by 2–3 orders of magnitude. It representsCC production of e, μ or τ . In particular the τ productionprocess (10) is expected to have a spectacular double bang sig-nature, resulting from the production and the hadronic decayvertices of τ , with a separation of ∼ 102 m in the multi-PeVenergy range of our interest [16]. This will constitute an im-portant bench-mark for the collinear triple bang signature forSUSY events, discussed below, as they would both have similardetection efficiencies.

The multi-PeV LSP, produced by the CC and NC processes(3), (4) is expected to decay mainly into the τ+τν and bbν

channels. The former decay leads to a collinear triple bangsignature, coming form the production vertex of (3), (4) andthe hadronic decay vertices of the two taus, again with typi-cal separations of ∼ 102 m. For a quantitative analysis, we haveperformed a Monte Carlo simulation of LSP production via (3),(4), followed by its decay, χ → τ+τ−ν. Each event recordsthe energies of the LSP as well as the two decay taus, and or-ders the latter according to their energies. Thus one gets theLorentz boosted decay range (r = r0E/m) of the LSP alongwith those of the more and less energetic taus. They are shownin Fig. 2 for an incident neutrino energy of 20 PeV, since most

of the signal events discussed below come from the lowest en-ergy bin, Eν = 20 ± 10 PeV. Note that the above LSP decayvertex is marked by the appearance of two collinear tau tracks,which may be hard to identify at the IceCube. Therefore wehave added the LSP range to those of the two decay taus andshown the resulting effective decay ranges of the more and theless energetic taus relative to the production vertex. Thus theyrepresent the ranges of the 2nd and 3rd collinear bangs rela-tive to the 1st. We see that for the MSSM spectra I and II theLSP decay range is peaked at 100 m, while the effective de-cay ranges of the two taus are peaked at 200 and 500 m. Thecorresponding ranges for the set III are reduced by about halfeach.

This is because the LSP carries most of the slepton energyfor the spectra I and II as they have similar masses, while forIII it carries about half the slepton energy. Note that all theseranges scale with the incident neutrino energy. Thus one canreduce the ranges by going to lower neutrino energy, which willin fact increase the signal rate.

It should be noted here that about 2/3rd of the signal cross-section comes from the CC process (3), which gives a multi-PeV charged lepton, collinear with the triple bang. This can beidentified via one more bang for tau, a clear track for muonand showering for electron. This constitutes an additional dis-tinctive feature of the above signal. This feature is even moreimportant for the χ → bbν decay channel, which would byitself show up as a double bang event. The presence of thecollinear multi-PeV charged lepton will give a third bang fortau, a clear track for muon or shower for electron. This canclearly distinguish this signal from the double bang events ofthe SM CC process (10), at least in the first two cases. In es-timating the signal size below we shall add 2/3rd of the BRfor this channel (40%) to the BR of the τ+τ−ν decay channel(30%), giving an effective BR of 70% for the SUSY signal.

It should be added here that the NC SUSY process (4) hasalso a distinct feature, in the sense that the first bang fromthe production vertex is followed by a clear gap of ≈ 100 m,corresponding to the decay range of the LSP χ . This can dis-tinguish the signal from the double bang events of the SM CCprocess (10), which are connected by the tau track, providedone can identify this track. However this may be quite hardat the IceCube, as mentioned earlier. It should also be notedthat the SUSY processes (3) and (4) have a second LSP, com-ing from the squark decay. The decay of this LSP (χ ) will giveadditional bang(s). Being a fragment of the nucleon target, how-ever, the squark and its decay products carry less energies thanthose of the slepton. Our Monte Carlo simulation shows thatthe LSP (χ ) and the resulting τ leptons from the squark de-cay have energies, which are smaller than the energies of thecorresponding particles from the slepton decay by about a fac-tor of 5 each. Accordingly the Lorentz boosted decay rangesof these particles are smaller by about a factor of 5 each rel-ative to the corresponding ones shown in Fig. 2. So only themore energetic τ lepton from the squark decay has a range ofabout 100 m from the production vertex, while the less ener-getic τ lepton and the LSP have decay ranges � 50 m from theproduction vertex. Hence only the more energetic τ lepton de-

188 M. Hirsch et al. / Physics Letters B 662 (2008) 185–189

cay will give an extra bang, which can be resolved from thatof the production vertex at the IceCube. One can easily checkthat including this extra bang from the squark decay τ does notlead to any significant enhancement of the signal BR. Thereforewe shall keep the above mentioned effective BR of 70% for theSUSY signal in this simple analysis.

Finally we come to the bad news, i.e. the event rate. It is es-timated by convoluting the above signal cross-section with theUHE neutrino flux, which is unfortunately clouded by a largeuncertainty. The most popular choice is the so-called Waxman–Bahcall (WB) flux, which assumes a common extragalacticsource for the UHE neutrinos and cosmic ray protons [17]. Itaccelerates protons to UHE, which then interacts with the ambi-ent photons to give pions, pγ → nπ+(pπ0), π+ → νμνμνee

+.The neutron escapes the confining magnetic field of the sourcealong with the neutrinos from pion decay. They further assumethe source to be optically thin, so that the neutron escapes with-out interaction with the ambient photons, and decays outside togive the CR proton. So the UHE neutrino and CR proton fluxesare correlated to one another. Finally they assume the typicalE−2 power law of a Fermi engine for the neutrino/CR spectra.The predicted neutrino flux, including all flavours of neutrinoand antineutrino, is

(12)J WBν = 6 × 10−8(E/GeV)−2 GeV−1 cm−2 s−1 sr−1,

which is equally distributed into the three flavours by neutrinooscillations. However the predicted normalisation has a ratherlarge model dependent uncertainty. Besides the assumed powerlaw of −2 has been questioned by many authors, who suggestto treat it instead as a free parameter [18]. Indeed as notedin [19], the AGASA and HiRes data [20] both show a steep-ening of the UHE CR spectrum from E−2 to E−2.54 aboveE = 3 × 108 GeV. This coincides with the change of CR com-position from heavy nuclei to proton dominance, marking thedominance of the extragalactic component. Based on this ob-servation these authors have used a WB type model to obtaina UHE neutrino flux from these CR data. They assume theabove photo-meson production process to be dominated by the�+ resonance, so that the energy sharing between the pion andthe neutron is kinematically determined. The pion is predictedto carry about 28% of the neutron energy and each of its de-cay neutrinos about 7% of the latter. Thus the CR proton fluxabove E ≈ 3 × 108 GeV determines the neutrino flux aboveEν ≈ 107 GeV. Using the average of AGASA and HiRes CRfluxes for normalisation, they predict a total neutrino flux forall flavours [19]

(13)J AH

ν (E) = 3.5 × 10−3(E/GeV)−2.54 GeV−1 cm−2 s−1 sr−1.

Apart from this there can be a contribution to the UHE neutrinoflux from optically thick sources like the cores of active galac-tic nuclei (AGN), from which no nucleon can escape [21]. Theonly particles coming out of the above mentioned photo-pionproduction process in these sources are the neutrinos and pho-tons resulting from the charged and neutral pion decays. Thusthe UHE neutrino flux in this case is correlated to a UHE pho-ton flux instead of CR. The photon flux cascades down to the

Table 1Predicted number of events for the 15 years of IceCube operation. The numberof signal events for SUSY spectra II (III) are 1/2 (1/10) of those shown forSUSY-I

Neutrino flux Waxman–Bahcall AGASA–HiRes AGN model

SM-τ (double bang) 12 65 ∼ 360SUSY-I 0.34 1.8 ∼ 10

GeV energy range in passage. Assuming the extragalactic com-ponent of the EGRET photon flux to be saturated by this contri-bution, gives an upper limit to this UHE neutrino flux, which isabout thirty times larger than the WB flux at Eν ≈ 20 PeV [21].

Since the earth is opaque to the neutrinos in the Eν � 10 PeVenergy range of our interest [22], we shall only consider thedown going neutrinos, covering a solid angle of 2π sr. Thenthe predicted number of signal events at IceCube is givenby

(14)N = 2πNT T

∫Jν(Eν)σ (Eν) dEν,

where NT = 6 × 1038 is the number of target nucleons in a km3

size ice/water telescope and T is its total operation time, whichwill be taken as 15 years. Table 1 shows the expected numberof signal events corresponding to the MSSM spectrum I alongwith those of the SM CC process (10) for the three UHE neu-trino fluxes mentioned above. We have incorporated the abovementioned BR of 0.7 for the former and the flavour factor of1/3 for the latter.

Note that the number of signal events in the bilinear RPBSUSY model considered here is the same as the standardMSSM. But unlike the latter the RPB model has a distinctivesignature at a UHE neutrino telescope, so that the viabilityof the signal is primarily determined by the number of sig-nal events. However the expected number of signal events atIceCube, shown in Table 1, is admittedly too small to give a vi-able SUSY signal. Even the most optimistic prediction of ∼ 10events may at best be marginally viable after taking into accountthe detection efficiency of IceCube. Nonetheless it is encourag-ing to note that the IceCube will at least come within strikingrange of detecting this SUSY signal. We hope that the suc-cessful operation of IceCube along with a similar sized waterCerenkov telescope at the Mediterranean will lead to construc-tion of a ∼ 10 km3 size UHE telescope in the future. Meanwhilethe UHE neutrino flux would have been measured at the Ice-Cube. So we hope that this telescope can effectively probe thisSUSY signal at least for the MSSM spectra I and II. As men-tioned before these two sets represent the most natural part ofthe SUSY parameter space, which may be hard to probe atLHC.

In summary, we have considered a predictive and well moti-vated extension of the MSSM, which has a distinctive signatureat the UHE neutrino telescopes. Admittedly the expected eventrate is at best marginal at the IceCube. But we hope that a∼ 10 km3 UHE neutrino telescope in the future will be able toprobe this signal more effectively, at least for a very importantpart of the SUSY parameter space.

M. Hirsch et al. / Physics Letters B 662 (2008) 185–189 189

Acknowledgements

We thank Manuel Drees, Raj Gandhi, Monoranjan Guchait,Francis Halzen, Sandip Pakvasa, Ricard Tomas and ThomasWeiler for discussions. This work was inspired by discussionsat the Aspen Institute 2007 Neutrino Physics Programme. Itwas supported by Spanish grants FPA2005-01269, FPA2005-25348-E(MEC), SAB2005-0131 and European CommissionContract MRTN-CT-2004-503369. D.P.R. was supported inpart by BRNS(DAE) through the Raja Ramanna Fellowship andby MEC SAB2005-0131.

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